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Cash flow analysis - Exam FM formula sheet

Every Exam FM formula in cash flow analysis on one printable sheet, condensed from the 4 reference pages that teach them.

4 topics, 13 formula lines. Every line is condensed from the Exam FM formula pages, which stay free to read in full. Print this page to get the sheet on paper; the site chrome drops away.

What is on this sheet

Cash flow analysis

Cash flow analysis

Net present value

NPV
NPV(i)=∑t≥0Ct vtNPV(i) = \sum_{t\ge 0} C_t\,v^{t}
Decision rule
NPV(i)>0⇒accept at required return iNPV(i) > 0 \Rightarrow \text{accept at required return } i
NPV is decreasing
ddiNPV(i)<0\dfrac{d}{di}NPV(i) < 0for a conventional project

IRR

Definition
NPV(i∗)=∑t≥0Ct(1+i∗)−t=0NPV(i^{*}) = \sum_{t\ge 0} C_t (1+i^{*})^{-t} = 0
Descartes' bound
#sign changes≥#positive roots\#\text{sign changes} \ge \#\text{positive roots}
Dollar-weighted (simple interest approximation)
i≈IA+∑tCt(1−t)i \approx \dfrac{I}{A + \sum_t C_t(1-t)}
Time-weighted
1+i=∏kBkBk−1+Ck−11 + i = \prod_k \dfrac{B_k}{B_{k-1} + C_{k-1}}

Spot rates

Present value
PV=∑tCt(1+st)tPV = \sum_{t} \dfrac{C_t}{(1+s_t)^{t}}
Zero-coupon price
P(t)=(1+st)−tP(t) = (1+s_t)^{-t}
Par yield
∑t=1nc(1+st)t+1(1+sn)n=1\sum_{t=1}^{n} \dfrac{c}{(1+s_t)^t} + \dfrac{1}{(1+s_n)^n} = 1solve for the coupon c that prices at par

Forward rates

Implied forward
(1+st2)t2=(1+st1)t1(1+ft1,t2)t2−t1(1+s_{t_2})^{t_2} = (1+s_{t_1})^{t_1}\left(1+f_{t_1,t_2}\right)^{t_2-t_1}
One-period forward
1+ft,t+1=(1+st+1)t+1(1+st)t1 + f_{t,t+1} = \dfrac{(1+s_{t+1})^{t+1}}{(1+s_t)^{t}}
Spot as a geometric mean
(1+sn)n=∏t=0n−1(1+ft,t+1)(1+s_n)^n = \prod_{t=0}^{n-1}\left(1+f_{t,t+1}\right)

Cash flow analysis - Exam FM formula sheet. Formulas condensed from the free reference pages on this site. Not affiliated with or endorsed by the Society of Actuaries.